For a set system $(V,{\mathcal C}\subseteq 2^V)$, we call a subset $C\in{\mathcal C}$ a component. A nonempty subset $Y\subseteq C$ is a minimal removable set (MRS) of $C$ if $C\setminus Y\in{\mathcal C}$ and no proper nonempty subset $Z\subsetneq Y$ satisfies $C\setminus Z\in{\mathcal C}$. In this paper, we consider the problem of enumerating all components in a set system such that, for every two components $C,C'\in{\mathcal C}$ with $C'\subsetneq C$, every MRS $X$ of $C$ satisfies either $X\subseteq C'$ or $X\cap C'=\emptyset$. We provide a partition-based algorithm for this problem, which yields the first linear delay algorithms to enumerate all 2-edge-connected induced subgraphs, and to enumerate all 2-vertex-connected induced subgraphs.

翻译：对于集合系统 $(V,{\mathcal C}\subseteq 2^V)$，我们称子集 $C\in{\mathcal C}$ 为一个分量。非空子集 $Y\subseteq C$ 是 $C$ 的最小可移除集 (MRS)，如果 $C\setminus Y\in{\mathcal C}$ 且不存在真非空子集 $Z\subsetneq Y$ 满足 $C\setminus Z\in{\mathcal C}$。本文考虑在集合系统中枚举所有分量的问题，其中对于任意两个满足 $C'\subsetneq C$ 的分量 $C,C'\in{\mathcal C}$，$C$ 的每个 MRS $X$ 要么满足 $X\subseteq C'$，要么满足 $X\cap C'=\emptyset$。我们针对该问题提出了一种基于划分的算法，该算法首次实现了枚举所有 2-边连通诱导子图以及枚举所有 2-顶点连通诱导子图的线性延迟。